%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV235+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:56:28 AM UTC 2026
% Result : Theorem 0.47s 0.42s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 18
% Syntax : Number of formulae : 148 ( 80 unt; 0 typ; 0 def)
% Number of atoms : 895 ( 242 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 1907 ( 314 ~; 216 |; 33 &;1320 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 13 con; 0-2 aty)
% Number of variables : 283 ( 0 ^; 283 !; 0 ?; 283 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_crypt,type,
crypt: $i > $i > $i ).
thf(tp_data,type,
data: $i ).
thf(tp_decrypt,type,
decrypt: $i > $i > $i ).
thf(tp_exp,type,
exp: $i ).
thf(tp_id,type,
id: $i ).
thf(tp_imp,type,
imp: $i ).
thf(tp_kek,type,
kek: $i ).
thf(tp_km,type,
km: $i ).
thf(tp_kp,type,
kp: $i ).
thf(tp_p,type,
p: $i > $o ).
thf(tp_pin,type,
pin: $i ).
thf(tp_pp,type,
pp: $i ).
thf(tp_rand,type,
rand: $i ).
thf(tp_xor,type,
xor: $i > $i > $i ).
thf(1,axiom,
p @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',an_account_number) ).
thf(2,axiom,
p @ exp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_11) ).
thf(7,axiom,
p @ ( crypt @ ( xor @ km @ pin ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_6) ).
thf(8,axiom,
p @ pin,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_5) ).
thf(9,axiom,
p @ id,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_4) ).
thf(10,axiom,
p @ data,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_3) ).
thf(11,axiom,
p @ imp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_2) ).
thf(12,axiom,
p @ kp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_1) ).
thf(13,axiom,
! [X1: $i,X2: $i] :
( ( ( p @ X2 )
& ( p @ X1 ) )
=> ( p @ ( crypt @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',encrypt_knowledge) ).
thf(14,axiom,
! [X1: $i,X2: $i] :
( ( ( p @ ( crypt @ X1 @ X2 ) )
& ( p @ X1 ) )
=> ( p @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',decrypt_knowledge) ).
thf(15,axiom,
! [X1: $i,X2: $i] :
( ( ( p @ X1 )
& ( p @ X2 ) )
=> ( p @ ( xor @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',combine_with_XOR) ).
thf(18,axiom,
! [X1: $i,Xk1: $i] :
( ( ( p @ X1 )
& ( p @ ( crypt @ ( xor @ km @ data ) @ Xk1 ) ) )
=> ( p @ ( crypt @ Xk1 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',encrypt_data) ).
thf(19,axiom,
! [Xk1: $i,Xtype: $i,Xk2: $i] :
( ( ( p @ Xk1 )
& ( p @ ( crypt @ ( xor @ km @ ( xor @ Xtype @ kp ) ) @ Xk2 ) )
& ( p @ Xtype ) )
=> ( p @ ( crypt @ ( xor @ km @ Xtype ) @ ( xor @ Xk2 @ Xk1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',key_part_import___part_3) ).
thf(20,axiom,
! [Xk1: $i,Xtype: $i,Xk2: $i] :
( ( ( p @ Xk1 )
& ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ Xtype ) ) @ Xk2 ) )
& ( p @ Xtype ) )
=> ( p @ ( crypt @ ( xor @ km @ ( xor @ Xtype @ kp ) ) @ ( xor @ Xk1 @ Xk2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',key_part_import___part_2) ).
thf(21,axiom,
! [Xk: $i,Xtype: $i] :
( ( ( p @ Xk )
& ( p @ Xtype ) )
=> ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ Xtype ) ) @ Xk ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',key_part_import___part_1) ).
thf(22,axiom,
! [Xtype: $i,Xk1: $i,Xkek1: $i] :
( ( ( p @ ( crypt @ ( xor @ km @ Xtype ) @ Xk1 ) )
& ( p @ Xtype )
& ( p @ ( crypt @ ( xor @ km @ exp ) @ Xkek1 ) ) )
=> ( p @ ( crypt @ ( xor @ Xkek1 @ Xtype ) @ Xk1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',key_export) ).
thf(26,axiom,
! [X1: $i,X2: $i] :
( ( decrypt @ X1 @ ( crypt @ X1 @ X2 ) )
= X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',encryption_decryption_cancellation) ).
thf(29,conjecture,
p @ ( crypt @ pp @ a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',find_pin) ).
thf(30,negated_conjecture,
( ( p @ ( crypt @ pp @ a ) )
= $false ),
inference(negate_conjecture,[status(cth)],[29]) ).
thf(31,plain,
( ( p @ ( crypt @ pp @ a ) )
= $false ),
inference(unfold_def,[status(thm)],[30]) ).
thf(32,plain,
( ( p @ a )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(33,plain,
( ( p @ exp )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(34,plain,
( ( p @ ( crypt @ ( xor @ km @ pin ) @ pp ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(35,plain,
( ( p @ pin )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(36,plain,
( ( p @ id )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(37,plain,
( ( p @ data )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(38,plain,
( ( p @ imp )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(39,plain,
( ( p @ kp )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(40,plain,
( ( ! [X1: $i,X2: $i] :
( ( ( p @ X2 )
& ( p @ X1 ) )
=> ( p @ ( crypt @ X1 @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(41,plain,
( ( ! [X1: $i,X2: $i] :
( ( ( p @ ( crypt @ X1 @ X2 ) )
& ( p @ X1 ) )
=> ( p @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(42,plain,
( ( ! [X1: $i,X2: $i] :
( ( ( p @ X1 )
& ( p @ X2 ) )
=> ( p @ ( xor @ X1 @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(43,plain,
( ( ! [X1: $i,Xk1: $i] :
( ( ( p @ X1 )
& ( p @ ( crypt @ ( xor @ km @ data ) @ Xk1 ) ) )
=> ( p @ ( crypt @ Xk1 @ X1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(44,plain,
( ( ! [Xk1: $i,Xtype: $i,Xk2: $i] :
( ( ( p @ Xk1 )
& ( p @ ( crypt @ ( xor @ km @ ( xor @ Xtype @ kp ) ) @ Xk2 ) )
& ( p @ Xtype ) )
=> ( p @ ( crypt @ ( xor @ km @ Xtype ) @ ( xor @ Xk2 @ Xk1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(45,plain,
( ( ! [Xk1: $i,Xtype: $i,Xk2: $i] :
( ( ( p @ Xk1 )
& ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ Xtype ) ) @ Xk2 ) )
& ( p @ Xtype ) )
=> ( p @ ( crypt @ ( xor @ km @ ( xor @ Xtype @ kp ) ) @ ( xor @ Xk1 @ Xk2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(46,plain,
( ( ! [Xk: $i,Xtype: $i] :
( ( ( p @ Xk )
& ( p @ Xtype ) )
=> ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ Xtype ) ) @ Xk ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(47,plain,
( ( ! [Xtype: $i,Xk1: $i,Xkek1: $i] :
( ( ( p @ ( crypt @ ( xor @ km @ Xtype ) @ Xk1 ) )
& ( p @ Xtype )
& ( p @ ( crypt @ ( xor @ km @ exp ) @ Xkek1 ) ) )
=> ( p @ ( crypt @ ( xor @ Xkek1 @ Xtype ) @ Xk1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(48,plain,
( ( ! [X1: $i,X2: $i] :
( ( decrypt @ X1 @ ( crypt @ X1 @ X2 ) )
= X2 ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(49,plain,
( ( ~ ( p @ ( crypt @ pp @ a ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[31]) ).
thf(50,plain,
( ( ! [X1: $i,X2: $i] :
( ( decrypt @ X1 @ ( crypt @ X1 @ X2 ) )
= X2 ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(51,plain,
( ( ! [Xtype: $i,Xk1: $i,Xkek1: $i] :
( ( ( p @ ( crypt @ ( xor @ km @ Xtype ) @ Xk1 ) )
& ( p @ Xtype )
& ( p @ ( crypt @ ( xor @ km @ exp ) @ Xkek1 ) ) )
=> ( p @ ( crypt @ ( xor @ Xkek1 @ Xtype ) @ Xk1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(52,plain,
( ( ! [Xk: $i,Xtype: $i] :
( ( ( p @ Xk )
& ( p @ Xtype ) )
=> ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ Xtype ) ) @ Xk ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(53,plain,
( ( ! [Xk1: $i,Xtype: $i,Xk2: $i] :
( ( ( p @ Xk1 )
& ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ Xtype ) ) @ Xk2 ) )
& ( p @ Xtype ) )
=> ( p @ ( crypt @ ( xor @ km @ ( xor @ Xtype @ kp ) ) @ ( xor @ Xk1 @ Xk2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(54,plain,
( ( ! [Xk1: $i,Xtype: $i,Xk2: $i] :
( ( ( p @ Xk1 )
& ( p @ ( crypt @ ( xor @ km @ ( xor @ Xtype @ kp ) ) @ Xk2 ) )
& ( p @ Xtype ) )
=> ( p @ ( crypt @ ( xor @ km @ Xtype ) @ ( xor @ Xk2 @ Xk1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(55,plain,
( ( ! [X1: $i,Xk1: $i] :
( ( ( p @ X1 )
& ( p @ ( crypt @ ( xor @ km @ data ) @ Xk1 ) ) )
=> ( p @ ( crypt @ Xk1 @ X1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(56,plain,
( ( ! [X1: $i,X2: $i] :
( ( ( p @ X1 )
& ( p @ X2 ) )
=> ( p @ ( xor @ X1 @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(57,plain,
( ( ! [X1: $i,X2: $i] :
( ( ( p @ ( crypt @ X1 @ X2 ) )
& ( p @ X1 ) )
=> ( p @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(58,plain,
( ( ! [X1: $i,X2: $i] :
( ( ( p @ X2 )
& ( p @ X1 ) )
=> ( p @ ( crypt @ X1 @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(59,plain,
( ( p @ kp )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(60,plain,
( ( p @ imp )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(61,plain,
( ( p @ data )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(62,plain,
( ( p @ id )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(63,plain,
( ( p @ pin )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(64,plain,
( ( p @ ( crypt @ ( xor @ km @ pin ) @ pp ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(65,plain,
( ( p @ exp )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(66,plain,
( ( p @ a )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(67,plain,
( ( ~ ( p @ ( crypt @ pp @ a ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(68,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ( p @ SX0 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SX1 ) ) @ SX2 ) ) )
| ~ ( p @ SX1 ) )
| ( p @ ( crypt @ ( xor @ km @ ( xor @ SX1 @ kp ) ) @ ( xor @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(69,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( p @ SX1 )
| ~ ( p @ SX0 ) )
| ( p @ ( crypt @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(70,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( p @ SX0 )
| ~ ( p @ ( crypt @ ( xor @ km @ data ) @ SX1 ) ) )
| ( p @ ( crypt @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(71,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ( p @ ( crypt @ ( xor @ km @ SX0 ) @ SX1 ) )
| ~ ( p @ SX0 ) )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SX2 ) ) )
| ( p @ ( crypt @ ( xor @ SX2 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(72,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( p @ ( crypt @ SX0 @ SX1 ) )
| ~ ( p @ SX0 ) )
| ( p @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(73,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ( p @ SX0 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ SX1 @ kp ) ) @ SX2 ) ) )
| ~ ( p @ SX1 ) )
| ( p @ ( crypt @ ( xor @ km @ SX1 ) @ ( xor @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(74,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( p @ SX0 )
| ~ ( p @ SX1 ) )
| ( p @ ( xor @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(75,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( p @ SX0 )
| ~ ( p @ SX1 ) )
| ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SX1 ) ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(76,plain,
! [SV1: $i] :
( ( ! [SY21: $i] :
( ( decrypt @ SV1 @ ( crypt @ SV1 @ SY21 ) )
= SY21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(77,plain,
( ( p @ ( crypt @ pp @ a ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(78,plain,
! [SV2: $i] :
( ( ! [SY22: $i,SY23: $i] :
( ~ ~ ( ~ ~ ( ~ ( p @ SV2 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SY22 ) ) @ SY23 ) ) )
| ~ ( p @ SY22 ) )
| ( p @ ( crypt @ ( xor @ km @ ( xor @ SY22 @ kp ) ) @ ( xor @ SV2 @ SY23 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(79,plain,
! [SV3: $i] :
( ( ! [SY24: $i] :
( ~ ~ ( ~ ( p @ SY24 )
| ~ ( p @ SV3 ) )
| ( p @ ( crypt @ SV3 @ SY24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(80,plain,
! [SV4: $i] :
( ( ! [SY25: $i] :
( ~ ~ ( ~ ( p @ SV4 )
| ~ ( p @ ( crypt @ ( xor @ km @ data ) @ SY25 ) ) )
| ( p @ ( crypt @ SY25 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(81,plain,
! [SV5: $i] :
( ( ! [SY26: $i,SY27: $i] :
( ~ ~ ( ~ ~ ( ~ ( p @ ( crypt @ ( xor @ km @ SV5 ) @ SY26 ) )
| ~ ( p @ SV5 ) )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SY27 ) ) )
| ( p @ ( crypt @ ( xor @ SY27 @ SV5 ) @ SY26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(82,plain,
! [SV6: $i] :
( ( ! [SY28: $i] :
( ~ ~ ( ~ ( p @ ( crypt @ SV6 @ SY28 ) )
| ~ ( p @ SV6 ) )
| ( p @ SY28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(83,plain,
! [SV7: $i] :
( ( ! [SY29: $i,SY30: $i] :
( ~ ~ ( ~ ~ ( ~ ( p @ SV7 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ SY29 @ kp ) ) @ SY30 ) ) )
| ~ ( p @ SY29 ) )
| ( p @ ( crypt @ ( xor @ km @ SY29 ) @ ( xor @ SY30 @ SV7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(84,plain,
! [SV8: $i] :
( ( ! [SY31: $i] :
( ~ ~ ( ~ ( p @ SV8 )
| ~ ( p @ SY31 ) )
| ( p @ ( xor @ SV8 @ SY31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(85,plain,
! [SV9: $i] :
( ( ! [SY32: $i] :
( ~ ~ ( ~ ( p @ SV9 )
| ~ ( p @ SY32 ) )
| ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SY32 ) ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(86,plain,
! [SV10: $i,SV1: $i] :
( ( ( decrypt @ SV1 @ ( crypt @ SV1 @ SV10 ) )
= SV10 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(87,plain,
! [SV11: $i,SV2: $i] :
( ( ! [SY33: $i] :
( ~ ~ ( ~ ~ ( ~ ( p @ SV2 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV11 ) ) @ SY33 ) ) )
| ~ ( p @ SV11 ) )
| ( p @ ( crypt @ ( xor @ km @ ( xor @ SV11 @ kp ) ) @ ( xor @ SV2 @ SY33 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(88,plain,
! [SV3: $i,SV12: $i] :
( ( ~ ~ ( ~ ( p @ SV12 )
| ~ ( p @ SV3 ) )
| ( p @ ( crypt @ SV3 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(89,plain,
! [SV13: $i,SV4: $i] :
( ( ~ ~ ( ~ ( p @ SV4 )
| ~ ( p @ ( crypt @ ( xor @ km @ data ) @ SV13 ) ) )
| ( p @ ( crypt @ SV13 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(90,plain,
! [SV14: $i,SV5: $i] :
( ( ! [SY34: $i] :
( ~ ~ ( ~ ~ ( ~ ( p @ ( crypt @ ( xor @ km @ SV5 ) @ SV14 ) )
| ~ ( p @ SV5 ) )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SY34 ) ) )
| ( p @ ( crypt @ ( xor @ SY34 @ SV5 ) @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(91,plain,
! [SV15: $i,SV6: $i] :
( ( ~ ~ ( ~ ( p @ ( crypt @ SV6 @ SV15 ) )
| ~ ( p @ SV6 ) )
| ( p @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(92,plain,
! [SV16: $i,SV7: $i] :
( ( ! [SY35: $i] :
( ~ ~ ( ~ ~ ( ~ ( p @ SV7 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ SV16 @ kp ) ) @ SY35 ) ) )
| ~ ( p @ SV16 ) )
| ( p @ ( crypt @ ( xor @ km @ SV16 ) @ ( xor @ SY35 @ SV7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(93,plain,
! [SV17: $i,SV8: $i] :
( ( ~ ~ ( ~ ( p @ SV8 )
| ~ ( p @ SV17 ) )
| ( p @ ( xor @ SV8 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(94,plain,
! [SV18: $i,SV9: $i] :
( ( ~ ~ ( ~ ( p @ SV9 )
| ~ ( p @ SV18 ) )
| ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV18 ) ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(95,plain,
! [SV19: $i,SV11: $i,SV2: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( p @ SV2 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV11 ) ) @ SV19 ) ) )
| ~ ( p @ SV11 ) )
| ( p @ ( crypt @ ( xor @ km @ ( xor @ SV11 @ kp ) ) @ ( xor @ SV2 @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(96,plain,
! [SV3: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( p @ SV12 )
| ~ ( p @ SV3 ) ) )
= $true )
| ( ( p @ ( crypt @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(97,plain,
! [SV13: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( p @ SV4 )
| ~ ( p @ ( crypt @ ( xor @ km @ data ) @ SV13 ) ) ) )
= $true )
| ( ( p @ ( crypt @ SV13 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(98,plain,
! [SV20: $i,SV14: $i,SV5: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( p @ ( crypt @ ( xor @ km @ SV5 ) @ SV14 ) )
| ~ ( p @ SV5 ) )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV20 ) ) )
| ( p @ ( crypt @ ( xor @ SV20 @ SV5 ) @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(99,plain,
! [SV15: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( p @ ( crypt @ SV6 @ SV15 ) )
| ~ ( p @ SV6 ) ) )
= $true )
| ( ( p @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(100,plain,
! [SV21: $i,SV16: $i,SV7: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( p @ SV7 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ SV16 @ kp ) ) @ SV21 ) ) )
| ~ ( p @ SV16 ) )
| ( p @ ( crypt @ ( xor @ km @ SV16 ) @ ( xor @ SV21 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(101,plain,
! [SV17: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( p @ SV8 )
| ~ ( p @ SV17 ) ) )
= $true )
| ( ( p @ ( xor @ SV8 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(102,plain,
! [SV18: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( p @ SV9 )
| ~ ( p @ SV18 ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV18 ) ) @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(103,plain,
! [SV19: $i,SV11: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( p @ SV2 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV11 ) ) @ SV19 ) ) )
| ~ ( p @ SV11 ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ SV11 @ kp ) ) @ ( xor @ SV2 @ SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(104,plain,
! [SV3: $i,SV12: $i] :
( ( ( ~ ( ~ ( p @ SV12 )
| ~ ( p @ SV3 ) ) )
= $false )
| ( ( p @ ( crypt @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(105,plain,
! [SV13: $i,SV4: $i] :
( ( ( ~ ( ~ ( p @ SV4 )
| ~ ( p @ ( crypt @ ( xor @ km @ data ) @ SV13 ) ) ) )
= $false )
| ( ( p @ ( crypt @ SV13 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(106,plain,
! [SV20: $i,SV14: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( p @ ( crypt @ ( xor @ km @ SV5 ) @ SV14 ) )
| ~ ( p @ SV5 ) )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV20 ) ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ SV20 @ SV5 ) @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(107,plain,
! [SV15: $i,SV6: $i] :
( ( ( ~ ( ~ ( p @ ( crypt @ SV6 @ SV15 ) )
| ~ ( p @ SV6 ) ) )
= $false )
| ( ( p @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(108,plain,
! [SV21: $i,SV16: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( p @ SV7 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ SV16 @ kp ) ) @ SV21 ) ) )
| ~ ( p @ SV16 ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ SV16 ) @ ( xor @ SV21 @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(109,plain,
! [SV17: $i,SV8: $i] :
( ( ( ~ ( ~ ( p @ SV8 )
| ~ ( p @ SV17 ) ) )
= $false )
| ( ( p @ ( xor @ SV8 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(110,plain,
! [SV18: $i,SV9: $i] :
( ( ( ~ ( ~ ( p @ SV9 )
| ~ ( p @ SV18 ) ) )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV18 ) ) @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(111,plain,
! [SV19: $i,SV11: $i,SV2: $i] :
( ( ( ~ ( ~ ~ ( ~ ( p @ SV2 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV11 ) ) @ SV19 ) ) )
| ~ ( p @ SV11 ) ) )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ SV11 @ kp ) ) @ ( xor @ SV2 @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(112,plain,
! [SV3: $i,SV12: $i] :
( ( ( ~ ( p @ SV12 )
| ~ ( p @ SV3 ) )
= $true )
| ( ( p @ ( crypt @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(113,plain,
! [SV13: $i,SV4: $i] :
( ( ( ~ ( p @ SV4 )
| ~ ( p @ ( crypt @ ( xor @ km @ data ) @ SV13 ) ) )
= $true )
| ( ( p @ ( crypt @ SV13 @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(114,plain,
! [SV20: $i,SV14: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( ~ ( p @ ( crypt @ ( xor @ km @ SV5 ) @ SV14 ) )
| ~ ( p @ SV5 ) )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV20 ) ) ) )
= $false )
| ( ( p @ ( crypt @ ( xor @ SV20 @ SV5 ) @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(115,plain,
! [SV15: $i,SV6: $i] :
( ( ( ~ ( p @ ( crypt @ SV6 @ SV15 ) )
| ~ ( p @ SV6 ) )
= $true )
| ( ( p @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(116,plain,
! [SV21: $i,SV16: $i,SV7: $i] :
( ( ( ~ ( ~ ~ ( ~ ( p @ SV7 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ SV16 @ kp ) ) @ SV21 ) ) )
| ~ ( p @ SV16 ) ) )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ SV16 ) @ ( xor @ SV21 @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(117,plain,
! [SV17: $i,SV8: $i] :
( ( ( ~ ( p @ SV8 )
| ~ ( p @ SV17 ) )
= $true )
| ( ( p @ ( xor @ SV8 @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(118,plain,
! [SV18: $i,SV9: $i] :
( ( ( ~ ( p @ SV9 )
| ~ ( p @ SV18 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV18 ) ) @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(119,plain,
! [SV19: $i,SV11: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( p @ SV2 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV11 ) ) @ SV19 ) ) )
| ~ ( p @ SV11 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ SV11 @ kp ) ) @ ( xor @ SV2 @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(120,plain,
! [SV3: $i,SV12: $i] :
( ( ( ~ ( p @ SV12 ) )
= $true )
| ( ( ~ ( p @ SV3 ) )
= $true )
| ( ( p @ ( crypt @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(121,plain,
! [SV13: $i,SV4: $i] :
( ( ( ~ ( p @ SV4 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ data ) @ SV13 ) ) )
= $true )
| ( ( p @ ( crypt @ SV13 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(122,plain,
! [SV20: $i,SV14: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( p @ ( crypt @ ( xor @ km @ SV5 ) @ SV14 ) )
| ~ ( p @ SV5 ) )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV20 ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ SV20 @ SV5 ) @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(123,plain,
! [SV15: $i,SV6: $i] :
( ( ( ~ ( p @ ( crypt @ SV6 @ SV15 ) ) )
= $true )
| ( ( ~ ( p @ SV6 ) )
= $true )
| ( ( p @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(124,plain,
! [SV21: $i,SV16: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( p @ SV7 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ SV16 @ kp ) ) @ SV21 ) ) )
| ~ ( p @ SV16 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ SV16 ) @ ( xor @ SV21 @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(125,plain,
! [SV17: $i,SV8: $i] :
( ( ( ~ ( p @ SV8 ) )
= $true )
| ( ( ~ ( p @ SV17 ) )
= $true )
| ( ( p @ ( xor @ SV8 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(126,plain,
! [SV18: $i,SV9: $i] :
( ( ( ~ ( p @ SV9 ) )
= $true )
| ( ( ~ ( p @ SV18 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV18 ) ) @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(127,plain,
! [SV19: $i,SV11: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( p @ SV2 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV11 ) ) @ SV19 ) ) ) )
= $true )
| ( ( ~ ( p @ SV11 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ SV11 @ kp ) ) @ ( xor @ SV2 @ SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(128,plain,
! [SV3: $i,SV12: $i] :
( ( ( p @ SV12 )
= $false )
| ( ( ~ ( p @ SV3 ) )
= $true )
| ( ( p @ ( crypt @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(129,plain,
! [SV13: $i,SV4: $i] :
( ( ( p @ SV4 )
= $false )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ data ) @ SV13 ) ) )
= $true )
| ( ( p @ ( crypt @ SV13 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(130,plain,
! [SV20: $i,SV14: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( p @ ( crypt @ ( xor @ km @ SV5 ) @ SV14 ) )
| ~ ( p @ SV5 ) ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV20 ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ SV20 @ SV5 ) @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(131,plain,
! [SV15: $i,SV6: $i] :
( ( ( p @ ( crypt @ SV6 @ SV15 ) )
= $false )
| ( ( ~ ( p @ SV6 ) )
= $true )
| ( ( p @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(132,plain,
! [SV21: $i,SV16: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( p @ SV7 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ SV16 @ kp ) ) @ SV21 ) ) ) )
= $true )
| ( ( ~ ( p @ SV16 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ SV16 ) @ ( xor @ SV21 @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(133,plain,
! [SV17: $i,SV8: $i] :
( ( ( p @ SV8 )
= $false )
| ( ( ~ ( p @ SV17 ) )
= $true )
| ( ( p @ ( xor @ SV8 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(134,plain,
! [SV18: $i,SV9: $i] :
( ( ( p @ SV9 )
= $false )
| ( ( ~ ( p @ SV18 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV18 ) ) @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(135,plain,
! [SV19: $i,SV11: $i,SV2: $i] :
( ( ( ~ ( ~ ( p @ SV2 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV11 ) ) @ SV19 ) ) ) )
= $false )
| ( ( ~ ( p @ SV11 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ SV11 @ kp ) ) @ ( xor @ SV2 @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(136,plain,
! [SV12: $i,SV3: $i] :
( ( ( p @ SV3 )
= $false )
| ( ( p @ SV12 )
= $false )
| ( ( p @ ( crypt @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(137,plain,
! [SV4: $i,SV13: $i] :
( ( ( p @ ( crypt @ ( xor @ km @ data ) @ SV13 ) )
= $false )
| ( ( p @ SV4 )
= $false )
| ( ( p @ ( crypt @ SV13 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(138,plain,
! [SV20: $i,SV14: $i,SV5: $i] :
( ( ( ~ ( ~ ( p @ ( crypt @ ( xor @ km @ SV5 ) @ SV14 ) )
| ~ ( p @ SV5 ) ) )
= $false )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV20 ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ SV20 @ SV5 ) @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(139,plain,
! [SV15: $i,SV6: $i] :
( ( ( p @ SV6 )
= $false )
| ( ( p @ ( crypt @ SV6 @ SV15 ) )
= $false )
| ( ( p @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(140,plain,
! [SV21: $i,SV16: $i,SV7: $i] :
( ( ( ~ ( ~ ( p @ SV7 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ SV16 @ kp ) ) @ SV21 ) ) ) )
= $false )
| ( ( ~ ( p @ SV16 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ SV16 ) @ ( xor @ SV21 @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(141,plain,
! [SV8: $i,SV17: $i] :
( ( ( p @ SV17 )
= $false )
| ( ( p @ SV8 )
= $false )
| ( ( p @ ( xor @ SV8 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(142,plain,
! [SV9: $i,SV18: $i] :
( ( ( p @ SV18 )
= $false )
| ( ( p @ SV9 )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV18 ) ) @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(143,plain,
! [SV19: $i,SV11: $i,SV2: $i] :
( ( ( ~ ( p @ SV2 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV11 ) ) @ SV19 ) ) )
= $true )
| ( ( ~ ( p @ SV11 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ SV11 @ kp ) ) @ ( xor @ SV2 @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(144,plain,
! [SV20: $i,SV14: $i,SV5: $i] :
( ( ( ~ ( p @ ( crypt @ ( xor @ km @ SV5 ) @ SV14 ) )
| ~ ( p @ SV5 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV20 ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ SV20 @ SV5 ) @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(145,plain,
! [SV21: $i,SV16: $i,SV7: $i] :
( ( ( ~ ( p @ SV7 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ SV16 @ kp ) ) @ SV21 ) ) )
= $true )
| ( ( ~ ( p @ SV16 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ SV16 ) @ ( xor @ SV21 @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(146,plain,
! [SV19: $i,SV11: $i,SV2: $i] :
( ( ( ~ ( p @ SV2 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV11 ) ) @ SV19 ) ) )
= $true )
| ( ( ~ ( p @ SV11 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ SV11 @ kp ) ) @ ( xor @ SV2 @ SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(147,plain,
! [SV20: $i,SV14: $i,SV5: $i] :
( ( ( ~ ( p @ ( crypt @ ( xor @ km @ SV5 ) @ SV14 ) ) )
= $true )
| ( ( ~ ( p @ SV5 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV20 ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ SV20 @ SV5 ) @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(148,plain,
! [SV21: $i,SV16: $i,SV7: $i] :
( ( ( ~ ( p @ SV7 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ SV16 @ kp ) ) @ SV21 ) ) )
= $true )
| ( ( ~ ( p @ SV16 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ SV16 ) @ ( xor @ SV21 @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(149,plain,
! [SV19: $i,SV11: $i,SV2: $i] :
( ( ( p @ SV2 )
= $false )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV11 ) ) @ SV19 ) ) )
= $true )
| ( ( ~ ( p @ SV11 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ SV11 @ kp ) ) @ ( xor @ SV2 @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(150,plain,
! [SV20: $i,SV14: $i,SV5: $i] :
( ( ( p @ ( crypt @ ( xor @ km @ SV5 ) @ SV14 ) )
= $false )
| ( ( ~ ( p @ SV5 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV20 ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ SV20 @ SV5 ) @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(151,plain,
! [SV21: $i,SV16: $i,SV7: $i] :
( ( ( p @ SV7 )
= $false )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ SV16 @ kp ) ) @ SV21 ) ) )
= $true )
| ( ( ~ ( p @ SV16 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ SV16 ) @ ( xor @ SV21 @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(152,plain,
! [SV2: $i,SV19: $i,SV11: $i] :
( ( ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV11 ) ) @ SV19 ) )
= $false )
| ( ( p @ SV2 )
= $false )
| ( ( ~ ( p @ SV11 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ SV11 @ kp ) ) @ ( xor @ SV2 @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(153,plain,
! [SV20: $i,SV14: $i,SV5: $i] :
( ( ( p @ SV5 )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ SV5 ) @ SV14 ) )
= $false )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV20 ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ SV20 @ SV5 ) @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(154,plain,
! [SV7: $i,SV21: $i,SV16: $i] :
( ( ( p @ ( crypt @ ( xor @ km @ ( xor @ SV16 @ kp ) ) @ SV21 ) )
= $false )
| ( ( p @ SV7 )
= $false )
| ( ( ~ ( p @ SV16 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ SV16 ) @ ( xor @ SV21 @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(155,plain,
! [SV19: $i,SV2: $i,SV11: $i] :
( ( ( p @ SV11 )
= $false )
| ( ( p @ SV2 )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV11 ) ) @ SV19 ) )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ SV11 @ kp ) ) @ ( xor @ SV2 @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(156,plain,
! [SV14: $i,SV5: $i,SV20: $i] :
( ( ( p @ ( crypt @ ( xor @ km @ exp ) @ SV20 ) )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ SV5 ) @ SV14 ) )
= $false )
| ( ( p @ SV5 )
= $false )
| ( ( p @ ( crypt @ ( xor @ SV20 @ SV5 ) @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(157,plain,
! [SV21: $i,SV7: $i,SV16: $i] :
( ( ( p @ SV16 )
= $false )
| ( ( p @ SV7 )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ SV16 @ kp ) ) @ SV21 ) )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ SV16 ) @ ( xor @ SV21 @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(158,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[59,157,156,155,142,141,139,137,136,86,77,66,65,64,63,62,61,60]) ).
thf(159,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[158]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV235+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.21 % Computer : n009.cluster.edu
% 0.07/0.21 % Model : x86_64 x86_64
% 0.07/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.21 % Memory : 8046.5625MB
% 0.07/0.21 % OS : Linux 6.8.0-71-generic
% 0.07/0.21 % CPULimit : 300
% 0.07/0.21 % WCLimit : 300
% 0.07/0.21 % DateTime : Tue Oct 6 16:21:02 UTC 2026
% 0.07/0.21 % CPUTime :
% 0.07/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.47/0.42
% 0.47/0.42 No.of.Axioms: 17
% 0.47/0.42
% 0.47/0.42 Length.of.Defs: 0
% 0.47/0.42
% 0.47/0.42 Contains.Choice.Funs: false
% 0.47/0.42 ....
% 0.47/0.42
% 0.47/0.42 ********************************
% 0.47/0.42 * All subproblems solved! *
% 0.47/0.42 ********************************
% 0.47/0.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:17,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:158,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.47/0.42
% 0.47/0.42 %**** Beginning of derivation protocol ****
% 0.47/0.42 % SZS output start CNFRefutation
% See solution above
% 0.47/0.42
% 0.47/0.42 %**** End of derivation protocol ****
% 0.47/0.42 %**** no. of clauses in derivation: 148 ****
% 0.47/0.42 %**** clause counter: 158 ****
% 0.47/0.42
% 0.47/0.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:17,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:158,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------